When the 10 km/hr bikes are 20 km apart, a bee begins flying from one wheel to the other at a steady speed of 30 km/hr. When it gets to the wheel it abruptly turns around and flies back to touch the first wheel, then turns around and keeps repeating the back-and-forth trip until the bikes meet, and squish!

How many kilometers did the bee travel in its total back-and forth trips?